Alex Schibli, owner of Rat Island in The Bronx, enjoys a summer picnic with his girlfriend Noelva Vigoya and nieces Melissa Lindahl (far left) and Stephanie Lindahl (far right). Schibli says he might build an eco-friendly house there — or he might just settle for getting the spot’s name changed back to its original moniker of Rattle Island. Photo: Rahav 'Iggy' Segev / Photopass.c

Alex Schibli, owner of Rat Island in The Bronx, enjoys a summer picnic with his girlfriend Noelva Vigoya and nieces Melissa Lindahl (far left) and Stephanie Lindahl (far right). Schibli says he might build an eco-friendly house there — or he might just settle for getting the spot’s name changed back to its original moniker of Rattle Island. (Rahav ‘Iggy’ Segev / Photopass.c)

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Clambering over the rocks like a schoolboy on an outdoor field trip, Alex Schibli points out three speckled eggs inside a nest.

“The seagulls are going to hatch in a day or two,” says the former Port Authority engineer, glancing at the sky as the expectant parents circle overhead.

“These birds are very respectful,” he says with a laugh. “When the owner [of the island] arrives, they leave for a little while, and then come back.”

That owner is Schibli, 72, who takes a deep breath of ocean air and beams with pride. Standing on the unfortunately named Rat Island, he feels like the luckiest man alive.

And with good reason. While most New Yorkers are busy carving out their own small turf on the isle of Manhattan, Schibli has his own private island at the northwestern end of Long Island Sound.

The softspoken Schibli paid $176,000 for the 2.5-acre slab of rock, beating out seven other bidders, including a fisherman and a nonprofit organization, in a sale last October. The island, which is zoned for residential use and costs $2,000 per year in taxes, was auctioned on behalf of the previous owner, 70-something retired businessman Edmund Brennan of Jupiter, Fla.

It’s believed to be the only truly privately owned island in the New York City archipelago of 44 islands, which includes Manhattan and Staten Island.

And as he prepares to enjoy his first summer of ownership, Schibli claims it was worth every cent.

“I read ‘Robinson Crusoe’ when I was a boy, [and] I was obsessed with ‘The Swiss Family Robinson,’ ” explains the 14-year City Island resident, whose house is situated about a quarter of a mile from his own island.

“I’d always dreamed of having my own place for peace and quiet in the middle of the ocean. When Rat Island came on the market, I had to buy it.”

So far, he’s added only an American flag and two “private property” signs to warn off unwanted visitors.

His main priority now: a new name. Schibli is trying to change the name back to Rattle Island, which originates from the 1600s, when Dutch mariners paid locals to use rattles to alert boat traffic to the treacherous rocks.

The term Rat Island also stems from folklore that 19th-century prisoners —

a k a “rats” — would hide on the rock while escaping from a jail on neighboring Hart Island.

As the new title holder, Schibli can apply to the authorities for permission to build a structure there — but for the moment, he wants to keep it as is. “Apart from the name change, I’m not really planning anything different for the island,” says the white-haired native of Switzerland, who specialized in energy conservation when he worked for the Port Authority.

“I love swimming, canoeing and collecting mussels — and we’re going to have lots of fun with my family. There’ll be picnics, barbecues and the occasional party, but, more than anything, we’re just going to relax.”

Schibli — who lives with his girlfriend, Noelva Vigoya, 61 — had a close call during the 9/11 attacks, a fact he prefers not to dwell on. His office was on the 82nd floor of the North Tower of the World Trade Center. He happened to be late for work that day, and arrived off the subway to witness the atrocity.

He says the experience made him look at his life and focus more on family.

“We’re a big, extended family with lots of grandchildren, nephews and nieces,” says Schibli, a father of four grown children who live in Germany, Switzerland and Washington, DC.

“Noelva and I will be inviting everyone out to Rat Island to enjoy the sunshine and the breeze and the beautiful views.”

And what views! Manhattan is obscured by City Island, but the rock offers spectacular vistas in all directions.

The pair are also working on an idea to eventually build a vacation home on the island, made of reclaimed wood and possibly on stilts, which would be off the grid — solar-powered and making use of collected rainwater.

“There are a lot of interesting designs out there,” says Schibli, a regular at conferences on eco-friendly, zero-energy housing.

“But people don’t have to worry. It will blend in with the scenery and won’t be an eyesore.”

The last house on Rat Island, once used as an artists’ hangout, was destroyed by a hurricane in 1938, but the stone foundations remain.

Schibli, who has been busy researching the island’s history on the Internet and at the New York Public Library and City Island Nautical Museum, loves one particular story from that era.

In December 1928, two hapless young men were marooned on the island for a freezing 15 hours when their boat ran aground and drifted off.

“They knocked on the door of the house, but nobody was in,” he laughs. “So they spent the night huddled under a rock.

“They were rescued the following morning.”

Of course, in this day and age, the castaways would likely have cellphones. “They would also just have broken into the house,” says Schibli. “And I can’t say I would blame them!”

As for Vigoya, she supported Schibli’s determination to buy the rock, but tried to talk him down from bidding more than $100,000 at last October’s auction.

“All the time, I was whispering in his ear, saying: ‘Stop, we can’t afford it!’ but, of course, he didn’t listen,” laughs Vigoya.

“He’d made up his mind, and nothing was going to stop him.”

At the time, she didn’t realize that Schibli, a hopeless romantic, had another motive in mind. “I always thought it would be a good place to host a wedding,” he says, mysteriously.